【摘要】 本文用孔隙介质力学的方法来研究纵波在介观周期成层Patchy模型的传播问题.相对于White方法,该方法少了不同介质分界面处的流体压力不等的假设,推导过程更为严密;和Dutta的双相方程解耦方法比较,文中方法直接求解双相方程,形式上更为直观.当纵波通过周期成层孔隙模型时,在低频段用孔隙弹性力学得到纵波频散和衰减结果与用White公式得到的结果符合得很好;周期成层的Patchy孔隙模型由于其空间排列的周期性使其成为孔隙弹性声子晶体,在其频散和衰减曲线上的高频段会出现多个禁带和通带,这使得速度不会随频率单调递增,衰减峰也不只一个.对于地震频段,随着渗透率降低模型的衰减峰向低频移动,这和实际观测结果一致,和传统Biot理论预测结果正相反;随着含气量上升纵波衰减峰值先上升后下降,其最大值出现在含气量0.1左右,这和相关实验结果一致.研究结果表明该模型可以定性解释观测到的地震衰减结果.更多还原

【Abstract】 In this paper poroelasticity is used to study the P wave propagation in periodic layered- model with patchy saturation at mesoscopic scale. Compared with the White s method, the deduction by the proposed method is more rigorous from mathematical view, without the assumption that the fluid pressures are not equal at the boundaries of different mediums as White has done. The proposed method solves the poroelastic equations in more directly perceived way than Dutta’ s mathematic techniques to make the equations uncoupled for solutions. When a P wave passes through the periodic layered-model with patchy saturation, the results of dispersion and attenuation by the method in this paper are consistent with those by White. Because of its periodic structure the patchy model becomes a phononic crystal with several passbands and stopbands in high frequency band. So the velocity of the P wave won t increase monotonously while the frequency increases, and there are several peaks of attenuation. As for seismic band, the attenuation peak of the patchy model moves to the low frequency as the permeability decreases, in accordance with the factual observation, but contrary to the results by Biot s theory before. When the gas volume rises in the model, the value of the attenuation peak increases at first, then decreases, and the maximum of the attenuation appears when the fraction of gas is nearly 0.1. The numerical results are in line with those by the related experiments. Researches show that the periodic layered-model with patchy saturation can qualitatively account for the observed seismic attenuation.更多还原